Abstract

We have investigated experimentally the linear and cubic nonlinear properties of multimode waveguides fabricated on AlGaAs wafers. By varying the input beam position or angle of incidence, the multipeak intensity profiles observed at the waveguide output unveil clearly the multimode nature of the waveguide. Because of the large Kerr nonlinearity of the semiconductor, the field evolution inside the waveguides depends on the launched intensity. Numerical simulations have confirmed the experimental findings and an analytical model, based on the nonlinear interaction between the modes of the dielectric structure, explains the device behavior and clarifies the role of the injected beam parameters.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. J. U. Kang, J. S. Aitchison, G. I. Stegeman, and N. Akhmediev, "One-dimensional spatial solitons in AlGaAs waveguides," Opt. Quantum Electron. 30, 649-671 (1998).
    [CrossRef]
  4. J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, "Experimental observation of spatial soliton interactions," Opt. Lett. 16, 15-17 (1991).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  6. J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
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    [CrossRef]
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  12. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
    [CrossRef]
  23. T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
    [CrossRef] [PubMed]
  24. J. S. Rodgers, S. E. Ralph, and R. P. Kenan, "Self-guiding multimode interference threshold switch," Opt. Lett. 25, 1717-1719 (2000).
    [CrossRef]
  25. Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, "All-optical mode mixer spatial switch based on cascading in lithium niobate," Appl. Phys. Lett. 72, 3405-3407 (1998).
    [CrossRef]
  26. A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809-1827 (1989).
    [CrossRef] [PubMed]
  27. S. Adachi, "GaAs, AlAs and AlxGa1−xAs: material parameters for use in research and device applications," J. Appl. Phys. 58, R1-R29 (1985).
    [CrossRef]
  28. M. Shamonin, M. Lohmeyer, and P. Hertel, "Analysis of power dependent switching between radiatively coupled planar waveguides," J. Lightwave Technol. 15, 983-989 (1997).
    [CrossRef]
  29. Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
    [CrossRef]
  30. N. Finlayson, E. M. Wright, C. T. Seaton, G. I. Stegeman, and Y. Silberberg, "Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide," Appl. Phys. Lett. 50, 1562-1564 (1987).
    [CrossRef]

2002 (3)

2000 (2)

J. S. Rodgers, S. E. Ralph, and R. P. Kenan, "Self-guiding multimode interference threshold switch," Opt. Lett. 25, 1717-1719 (2000).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

1999 (1)

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

1998 (3)

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, "All-optical mode mixer spatial switch based on cascading in lithium niobate," Appl. Phys. Lett. 72, 3405-3407 (1998).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

J. U. Kang, J. S. Aitchison, G. I. Stegeman, and N. Akhmediev, "One-dimensional spatial solitons in AlGaAs waveguides," Opt. Quantum Electron. 30, 649-671 (1998).
[CrossRef]

1997 (2)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The nonlinear optical properties of AlGaAs at the half band gap," IEEE J. Quantum Electron. 33, 341-348 (1997).
[CrossRef]

M. Shamonin, M. Lohmeyer, and P. Hertel, "Analysis of power dependent switching between radiatively coupled planar waveguides," J. Lightwave Technol. 15, 983-989 (1997).
[CrossRef]

1996 (2)

J. U. Kang, G. I. Stegeman, and J. S. Aitchison, "One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides," Opt. Lett. 21, 189-191 (1996).
[CrossRef] [PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

1995 (1)

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (5)

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightwave Technol. 10, 1843-1850 (1992).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, "Effects of three-photon absorption on nonlinear directional coupling," Opt. Lett. 17, 710-712 (1992).
[CrossRef] [PubMed]

K. Al-Hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, "Ultrafast all-optical switching in GaAlAs integrated interferometer in 1.55 µm spectral region," Electron. Lett. 28, 1090-1092 (1992).
[CrossRef]

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, "Observation of spatial solitons in AlGaAs waveguides," Electron. Lett. 28, 1879-1880 (1992).
[CrossRef]

1991 (2)

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, "Experimental observation of spatial soliton interactions," Opt. Lett. 16, 15-17 (1991).
[CrossRef] [PubMed]

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

1989 (1)

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809-1827 (1989).
[CrossRef] [PubMed]

1987 (2)

Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
[CrossRef]

N. Finlayson, E. M. Wright, C. T. Seaton, G. I. Stegeman, and Y. Silberberg, "Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide," Appl. Phys. Lett. 50, 1562-1564 (1987).
[CrossRef]

1985 (1)

S. Adachi, "GaAs, AlAs and AlxGa1−xAs: material parameters for use in research and device applications," J. Appl. Phys. 58, R1-R29 (1985).
[CrossRef]

1978 (1)

1975 (1)

R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
[CrossRef]

Aceves, A. B.

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809-1827 (1989).
[CrossRef] [PubMed]

Adachi, S.

S. Adachi, "GaAs, AlAs and AlxGa1−xAs: material parameters for use in research and device applications," J. Appl. Phys. 58, R1-R29 (1985).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, R. Morandotti, Y. Silberberg, J. M. Arnold, G. Pennelli, and J. S. Aitchison, "Optical discrete solitons in waveguide arrays. 1. Soliton formation," J. Opt. Soc. Am. B 19, 2938-2944 (2002).
[CrossRef]

U. Peschel, R. Morandotti, J. M. Arnold, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, T. Pertsch, and F. Lederer, "Optical discrete solitons in waveguide arrays. 2. Dynamic properties," J. Opt. Soc. Am. B 19, 2637-2644 (2002).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

J. U. Kang, J. S. Aitchison, G. I. Stegeman, and N. Akhmediev, "One-dimensional spatial solitons in AlGaAs waveguides," Opt. Quantum Electron. 30, 649-671 (1998).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The nonlinear optical properties of AlGaAs at the half band gap," IEEE J. Quantum Electron. 33, 341-348 (1997).
[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

J. U. Kang, G. I. Stegeman, and J. S. Aitchison, "One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides," Opt. Lett. 21, 189-191 (1996).
[CrossRef] [PubMed]

J. S. Aitchison, A. Villeneuve, and G. I. Stegeman, "All-optical switching in a nonlinear GaAlAs X junction," Opt. Lett. 18, 1153-1155 (1993).
[CrossRef] [PubMed]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, "Effects of three-photon absorption on nonlinear directional coupling," Opt. Lett. 17, 710-712 (1992).
[CrossRef] [PubMed]

K. Al-Hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, "Ultrafast all-optical switching in GaAlAs integrated interferometer in 1.55 µm spectral region," Electron. Lett. 28, 1090-1092 (1992).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, "Observation of spatial solitons in AlGaAs waveguides," Electron. Lett. 28, 1879-1880 (1992).
[CrossRef]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, "Experimental observation of spatial soliton interactions," Opt. Lett. 16, 15-17 (1991).
[CrossRef] [PubMed]

Akhmediev, N.

J. U. Kang, J. S. Aitchison, G. I. Stegeman, and N. Akhmediev, "One-dimensional spatial solitons in AlGaAs waveguides," Opt. Quantum Electron. 30, 649-671 (1998).
[CrossRef]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

Al-Hemyari, K.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, "Observation of spatial solitons in AlGaAs waveguides," Electron. Lett. 28, 1879-1880 (1992).
[CrossRef]

K. Al-Hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, "Ultrafast all-optical switching in GaAlAs integrated interferometer in 1.55 µm spectral region," Electron. Lett. 28, 1090-1092 (1992).
[CrossRef]

Andreadakis, N. C.

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Ankele, G.

R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
[CrossRef]

Arnold, J. M.

Assanto, G.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, "All-optical mode mixer spatial switch based on cascading in lithium niobate," Appl. Phys. Lett. 72, 3405-3407 (1998).
[CrossRef]

Bachmann, M.

Baek, Y.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, "All-optical mode mixer spatial switch based on cascading in lithium niobate," Appl. Phys. Lett. 72, 3405-3407 (1998).
[CrossRef]

Besse, P. A.

Bhat, R.

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

Bräuer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Deri, R. J.

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Dries, C.

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Dubost, A. H.

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightwave Technol. 10, 1843-1850 (1992).
[CrossRef]

Eisenberg, H. S.

Finlayson, N.

N. Finlayson, E. M. Wright, C. T. Seaton, G. I. Stegeman, and Y. Silberberg, "Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide," Appl. Phys. Lett. 50, 1562-1564 (1987).
[CrossRef]

Forrest, S.

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Grant, R. S.

K. Al-Hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, "Ultrafast all-optical switching in GaAlAs integrated interferometer in 1.55 µm spectral region," Electron. Lett. 28, 1090-1092 (1992).
[CrossRef]

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, "Observation of spatial solitons in AlGaAs waveguides," Electron. Lett. 28, 1879-1880 (1992).
[CrossRef]

Hawkins, R. J.

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Hayes, T. R.

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Hertel, P.

M. Shamonin, M. Lohmeyer, and P. Hertel, "Analysis of power dependent switching between radiatively coupled planar waveguides," J. Lightwave Technol. 15, 983-989 (1997).
[CrossRef]

Hutchings, D. C.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The nonlinear optical properties of AlGaAs at the half band gap," IEEE J. Quantum Electron. 33, 341-348 (1997).
[CrossRef]

Hyun Park, K.

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Ironside, C. N.

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, "Observation of spatial solitons in AlGaAs waveguides," Electron. Lett. 28, 1879-1880 (1992).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

K. Al-Hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, "Ultrafast all-optical switching in GaAlAs integrated interferometer in 1.55 µm spectral region," Electron. Lett. 28, 1090-1092 (1992).
[CrossRef]

Jackel, J. L.

Kamiya, T.

Kang, J. U.

J. U. Kang, J. S. Aitchison, G. I. Stegeman, and N. Akhmediev, "One-dimensional spatial solitons in AlGaAs waveguides," Opt. Quantum Electron. 30, 649-671 (1998).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The nonlinear optical properties of AlGaAs at the half band gap," IEEE J. Quantum Electron. 33, 341-348 (1997).
[CrossRef]

J. U. Kang, G. I. Stegeman, and J. S. Aitchison, "One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides," Opt. Lett. 21, 189-191 (1996).
[CrossRef] [PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

Kenan, R. P.

Kennedy, G. T.

K. Al-Hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, "Ultrafast all-optical switching in GaAlAs integrated interferometer in 1.55 µm spectral region," Electron. Lett. 28, 1090-1092 (1992).
[CrossRef]

Leaird, D. E.

Lederer, F.

Levy, D. S.

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Lohmeyer, M.

M. Shamonin, M. Lohmeyer, and P. Hertel, "Analysis of power dependent switching between radiatively coupled planar waveguides," J. Lightwave Technol. 15, 983-989 (1997).
[CrossRef]

Melchior, H.

Moloney, J. V.

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809-1827 (1989).
[CrossRef] [PubMed]

Morandotti, R.

Newell, A. C.

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809-1827 (1989).
[CrossRef] [PubMed]

Oliver, M. K.

Osgood, R. M.

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Pennelli, G.

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightwave Technol. 10, 1843-1850 (1992).
[CrossRef]

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Pertsch, T.

Peschel, U.

Ralph, S. E.

Rodgers, J. S.

Scarmozzino, R.

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Scherer, A.

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Schiek, R.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, "All-optical mode mixer spatial switch based on cascading in lithium niobate," Appl. Phys. Lett. 72, 3405-3407 (1998).
[CrossRef]

Seaton, C. T.

N. Finlayson, E. M. Wright, C. T. Seaton, G. I. Stegeman, and Y. Silberberg, "Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide," Appl. Phys. Lett. 50, 1562-1564 (1987).
[CrossRef]

Shamonin, M.

M. Shamonin, M. Lohmeyer, and P. Hertel, "Analysis of power dependent switching between radiatively coupled planar waveguides," J. Lightwave Technol. 15, 983-989 (1997).
[CrossRef]

Sibbett, W.

K. Al-Hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, "Ultrafast all-optical switching in GaAlAs integrated interferometer in 1.55 µm spectral region," Electron. Lett. 28, 1090-1092 (1992).
[CrossRef]

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, "Observation of spatial solitons in AlGaAs waveguides," Electron. Lett. 28, 1879-1880 (1992).
[CrossRef]

Silberberg, Y.

Silberberg , Y.

Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
[CrossRef]

Silberberg, Y.

N. Finlayson, E. M. Wright, C. T. Seaton, G. I. Stegeman, and Y. Silberberg, "Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide," Appl. Phys. Lett. 50, 1562-1564 (1987).
[CrossRef]

Smit, M. K.

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightwave Technol. 10, 1843-1850 (1992).
[CrossRef]

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Smith, P. W. E.

Sohler, W.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, "All-optical mode mixer spatial switch based on cascading in lithium niobate," Appl. Phys. Lett. 72, 3405-3407 (1998).
[CrossRef]

Soldano , L. B.

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

Soldano, L. B.

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightwave Technol. 10, 1843-1850 (1992).
[CrossRef]

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Stegeman, G.

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, "All-optical mode mixer spatial switch based on cascading in lithium niobate," Appl. Phys. Lett. 72, 3405-3407 (1998).
[CrossRef]

Stegeman, G. I.

J. U. Kang, J. S. Aitchison, G. I. Stegeman, and N. Akhmediev, "One-dimensional spatial solitons in AlGaAs waveguides," Opt. Quantum Electron. 30, 649-671 (1998).
[CrossRef]

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The nonlinear optical properties of AlGaAs at the half band gap," IEEE J. Quantum Electron. 33, 341-348 (1997).
[CrossRef]

J. U. Kang, G. I. Stegeman, and J. S. Aitchison, "One-dimensional spatial soliton dragging, trapping, and all-optical switching in AlGaAs waveguides," Opt. Lett. 21, 189-191 (1996).
[CrossRef] [PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

J. S. Aitchison, A. Villeneuve, and G. I. Stegeman, "All-optical switching in a nonlinear GaAlAs X junction," Opt. Lett. 18, 1153-1155 (1993).
[CrossRef] [PubMed]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, "Effects of three-photon absorption on nonlinear directional coupling," Opt. Lett. 17, 710-712 (1992).
[CrossRef] [PubMed]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
[CrossRef]

N. Finlayson, E. M. Wright, C. T. Seaton, G. I. Stegeman, and Y. Silberberg, "Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide," Appl. Phys. Lett. 50, 1562-1564 (1987).
[CrossRef]

Studenkov, P.

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

Ulrich , R.

R. Ulrich and T. Kamiya, "Resolution of self-images in pla- nar optical waveguides," J. Opt. Soc. Am. 68, 583-592 (1978).
[CrossRef]

R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
[CrossRef]

Veerman, F. B.

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightwave Technol. 10, 1843-1850 (1992).
[CrossRef]

Verbeek, B. H.

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightwave Technol. 10, 1843-1850 (1992).
[CrossRef]

Villeneuve, A.

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The nonlinear optical properties of AlGaAs at the half band gap," IEEE J. Quantum Electron. 33, 341-348 (1997).
[CrossRef]

J. S. Aitchison, A. Villeneuve, and G. I. Stegeman, "All-optical switching in a nonlinear GaAlAs X junction," Opt. Lett. 18, 1153-1155 (1993).
[CrossRef] [PubMed]

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, "Effects of three-photon absorption on nonlinear directional coupling," Opt. Lett. 17, 710-712 (1992).
[CrossRef] [PubMed]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

Weiner, A. M.

Wigley, P. G. J.

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

Wright, E. M.

N. Finlayson, E. M. Wright, C. T. Seaton, G. I. Stegeman, and Y. Silberberg, "Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide," Appl. Phys. Lett. 50, 1562-1564 (1987).
[CrossRef]

Yang, C. C.

C. C. Yang, A. Villeneuve, G. I. Stegeman, and J. S. Aitchison, "Effects of three-photon absorption on nonlinear directional coupling," Opt. Lett. 17, 710-712 (1992).
[CrossRef] [PubMed]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (6)

E. C. M. Pennings, R. J. Deri, A. Scherer, R. Bhat, T. R. Hayes, N. C. Andreadakis, M. K. Smit, L. B. Soldano, and R. J. Hawkins, "Ultracompact, low-loss directional couplers on InP based on self-imaging by multimode interference," Appl. Phys. Lett. 59, 1926-1928 (1991).
[CrossRef]

Y. Baek, R. Schiek, G. Stegeman, G. Assanto, and W. Sohler, "All-optical mode mixer spatial switch based on cascading in lithium niobate," Appl. Phys. Lett. 72, 3405-3407 (1998).
[CrossRef]

Y. Silberberg and G. I. Stegeman, "Nonlinear coupling of waveguide modes," Appl. Phys. Lett. 50, 801-803 (1987).
[CrossRef]

N. Finlayson, E. M. Wright, C. T. Seaton, G. I. Stegeman, and Y. Silberberg, "Beam propagation study of nonlinear coupling between transverse electric modes of a slab waveguide," Appl. Phys. Lett. 50, 1562-1564 (1987).
[CrossRef]

A. Villeneuve, C. C. Yang, P. G. J. Wigley, G. I. Stegeman, J. S. Aitchison, and C. N. Ironside, "Ultrafast all-optical switching in semiconductor nonlinear directional couplers at half the band gap," Appl. Phys. Lett. 61, 147-149 (1992).
[CrossRef]

R. Ulrich and G. Ankele, "Self-imaging in homogeneous planar optical waveguides," Appl. Phys. Lett. 27, 337-339 (1975).
[CrossRef]

Electron. Lett. (2)

K. Al-Hemyari, J. S. Aitchison, C. N. Ironside, G. T. Kennedy, R. S. Grant, and W. Sibbett, "Ultrafast all-optical switching in GaAlAs integrated interferometer in 1.55 µm spectral region," Electron. Lett. 28, 1090-1092 (1992).
[CrossRef]

J. S. Aitchison, K. Al-Hemyari, C. N. Ironside, R. S. Grant, and W. Sibbett, "Observation of spatial solitons in AlGaAs waveguides," Electron. Lett. 28, 1879-1880 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. S. Aitchison, D. C. Hutchings, J. U. Kang, G. I. Stegeman, and A. Villeneuve, "The nonlinear optical properties of AlGaAs at the half band gap," IEEE J. Quantum Electron. 33, 341-348 (1997).
[CrossRef]

IEEE Photonics Technol. Lett. (1)

D. S. Levy, K. Hyun Park, R. Scarmozzino, R. M. Osgood, C. Dries, P. Studenkov, and S. Forrest, "Fabrication of ultracompact 3-dB 2×2 MMI power splitters," IEEE Photonics Technol. Lett. 11, 1009-1011 (1999).
[CrossRef]

J. Appl. Phys. (1)

S. Adachi, "GaAs, AlAs and AlxGa1−xAs: material parameters for use in research and device applications," J. Appl. Phys. 58, R1-R29 (1985).
[CrossRef]

J. Lightwave Technol. (3)

M. Shamonin, M. Lohmeyer, and P. Hertel, "Analysis of power dependent switching between radiatively coupled planar waveguides," J. Lightwave Technol. 15, 983-989 (1997).
[CrossRef]

L. B. Soldano and E. C. M. Pennings, "Optical multi-mode interference devices based on self-imaging: principles and applications," J. Lightwave Technol. 13, 615-627 (1995).
[CrossRef]

L. B. Soldano, F. B. Veerman, M. K. Smit, B. H. Verbeek, A. H. Dubost, and E. C. M. Pennings, "Planar monomode optical couplers based on multimode interference effects," J. Lightwave Technol. 10, 1843-1850 (1992).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

Opt. Lett. (5)

Opt. Quantum Electron. (1)

J. U. Kang, J. S. Aitchison, G. I. Stegeman, and N. Akhmediev, "One-dimensional spatial solitons in AlGaAs waveguides," Opt. Quantum Electron. 30, 649-671 (1998).
[CrossRef]

Phys. Rev. A (1)

A. B. Aceves, J. V. Moloney, and A. C. Newell, "Theory of light-beam propagation at nonlinear interfaces. I. Equivalent-particle theory for a single interface," Phys. Rev. A 39, 1809-1827 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (4)

T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, and F. Lederer, "Anomalous refraction and diffraction in discrete optical systems," Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, "Observation of Manakov spatial solitons in AlGaAs planar waveguides," Phys. Rev. Lett. 76, 3699-3702 (1996).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383-3386 (1998).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863-1866 (2000).
[CrossRef] [PubMed]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1995).

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Figures (11)

Fig. 1
Fig. 1

Ridge waveguide cross section and top view of the equivalent slab waveguide. W is the width of the ridge and of the equivalent slab core.

Fig. 2
Fig. 2

Calculated initial moduli |Mp(0)| of the excited modes for different tilt angles: θ=0° (circles), θ=1° (squares), θ=2° (diamonds). The wavelength is λ=1530 nm, the beam FWHM is 15 µm, the slab core width is W=30 µm, and the core and cladding refractive indices are nr=3.331 and n0=3.326, respectively.

Fig. 3
Fig. 3

Calculated initial moduli |Mp(0)| of the excited modes for different beam FWHMs: 20 µm (circles), 15 µm (squares), 10 µm (diamonds). The wavelength is λ=1530 nm, the tilt angle is θ=1.5°, the slab core width is W=30 µm, and the core and cladding refractive indices are nr=3.331 and n0=3.326, respectively.

Fig. 4
Fig. 4

Schematic drawing of the experimental setup; the microscope slide in front of the input microscope objective is used to tilt the injected beam.

Fig. 5
Fig. 5

Measured intensity at the waveguide output facet versus the input beam center position. The light intensity is shown on a gray scale. The white dashed lines show the ridge edge positions.

Fig. 6
Fig. 6

Output intensity profiles, measured with an infrared camera, for tilt angles (from bottom to top) of θ=0°, 0.2°, 0.4°, 0.5°, 0.7°, 0.9°, 1.0°. The solid curves refer to the linear regime and the dashed curves to the input beam with a peak power of 700 W. The thin vertical lines show the ridge edge positions. The waveguide is 3 mm long.

Fig. 7
Fig. 7

Output intensity profiles, measured with an infrared camera, for θ=1.2°, 1.4°, 1.6°, 1.7°, 2.0°, 2.4°, and 2.5°. The solid curves refer to the linear regime and the dashed curves to the input beam with a peak power of 700 W. The thin vertical lines show the ridge edge positions. The waveguide is 3 mm long.

Fig. 8
Fig. 8

Simulated field intensity evolution inside the waveguide for θ=1.3° and different input powers: (a) 1 W, (b) 350 W, (c) 700 W. The equivalent slab core width is W=30 µm and the white dashed lines show its position; the core and cladding refractive indices are nr=3.331 and n0=3.326, respectively.

Fig. 9
Fig. 9

Numerically calculated output intensity profiles for four different tilt angles: θ=0.4°, 1.1°, 1.5° and 2.4°. Results for the linear case (solid curves) are compared with the profiles for an input power of 350 W (dashed curves). The thin vertical lines show the ridge edge positions.

Fig. 10
Fig. 10

Evolution of the three most relevant mode amplitudes (|Mp| with p=0, 2, 4) for θ=0° and an input power level of 700 W. The solid curves are the results from the coupled equations and the dashed curves are calculated by means of the BPM.

Fig. 11
Fig. 11

Evolution of the five most intense mode amplitudes (|Mp| with p=0, 1, 2, 3, 4) for θ=1° and an input power of 700 W. The solid curves are the results from the coupled equations and the dashed curves are obtained from the BPM simulations.

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

Ep(z, x)=Mp(z)Ep(x)p=0,, N-1.
Ep(x)=2W sinπW(p+1)x+W2if-W2<x<W2
Ep(x)=0elsewhere.
βp=2πλnr2-(p+1)2π2W21/22πλnr-(p+1)2πλ4nrW2,
N-12Wλ nr2-n021/2<N.
-Ep(x)Eq(x)dx=0pq,
Mp(0)=-Ep(x)Ein(x)dx-Ep2(x)dx.
i dMpdz+βpMp=0p=0,, N-1,
E(z, x)=p=0N-1Mp(z)Ep(x),
Lπ=4nrW23λ.
Ein(x)=E0 exp-(x-x0)22X02+i 2πnrλ sin(θ)x,
i Ez+12k 2Ex2+12kn(x)n02-1E+k n2n0|E|2E
=0,
2E˜z2+2E˜x2-μ0 2t2[0n2(x)E˜+0χ(3)E˜3]=0,
2iβ0 Ez+2Ex2-β02E+k2n2(x)E
+ω2μ00χ(3) 34E2E*=0.
i Mpz+(βp2-β02)2β0Mp
+38 ω2μ00β0χ(3)q,r,s=0N-1CpqrsMqMrMs*=0,
Cpqrs=-Ep(x)Eq(x)Er(x)Es(x)dx-Ep2(x)dx.

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